What’s the difference between いっぱい vs たくさん in Japanese?

Both can be translated as:

• A lot
• Many
• Much

たくさん

• usually refers to something is “enough”.
• usually for countable things.

いっぱい

• refers to something is complete or full, or there’s no more availability or space.
• usually for uncountable things e.g. liquids.

Examples

仕事のことで頭がいっぱい。
I’m occupied with thinking about work.

そばをたくさん食べました。
I ate a lot of soba noodles (but I still have room for dessert).

そばをいっぱい食べました。
I had too many soba noodles (and I can’t eat any more).

お腹がいっぱい。
I’m full now.

予約がいっぱい。
Fully booked.

予約がたくさん。
There are many bookings (but there’s still vacancy).